Cadence APS vs XPS vs AMS

Cadence Spectre APS : Spectre Accelerated Parallel Simulator

Cadence Spectre XPS : Spectre eXtensive Partitioning Simulator

Cadence Spectre AMS Designer : Spectre AMS Designer Simulator

If you want to read the official documents about these three simulators, please visit cadence link.
You can also get a cadence tutorial file named: Spectre Circuit Simulator Reference from Cadence Support.
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Spectre XPS is a FastSPICE circuit simulator that uses techniques like partitioning in order to simulate large, extracted netlists with 10's of millions of elements, and allowing IR drop analysis for extracted netlists.

Spectre APS is used for smaller designs and for highest accuracy circuits like: BER of an ADC, PLL jitter. It can be used without issues in transient analysis. (More discussions about APS, please email me.)

For introduction of AMS simulator, you can view ECEN 5007 course website of Prof. Hanh-Phuc Le.